A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties

At a Glance

Metadata	Details
Publication Date	2019-11-27
Journal	Journal of Physics Condensed Matter
Authors	Zheyong Fan, Yanzhou Wang, Xiaokun Gu, Ping Qian, Yanjing Su
Institutions	Loughborough University, Shanghai Jiao Tong University
Citations	18
Analysis	Full AI Review Included

Technical Documentation & Analysis: Minimal Tersoff Potential for Diamond Silicon

This document analyzes the research paper “A minimal Tersoff potential for diamond silicon with improved descriptions of elastic and phonon transport properties” and outlines how 6CCVD’s advanced MPCVD diamond materials and engineering services can support and extend this critical work in thermal physics and materials modeling.

Executive Summary

Core Achievement: Researchers successfully developed a minimal, six-parameter Tersoff potential for diamond silicon (Si) that accurately models elastic constants, phonon dispersion, and thermal conductivity ($\kappa$).
Improved Accuracy: The new potential significantly improves the prediction of thermal conductivity, overshooting the experimental value at 700 K by only ~20%, compared to previous models that overshot by up to 80% or underestimated by factors of 2 to 5.
Phonon Transport: The minimal potential provides the best description of phonon dispersion curves among all empirical potentials tested, which is crucial for accurate thermal transport modeling.
Quantum Effects Quantified: The study confirmed that using classical statistics underestimates the thermal conductivity of diamond silicon by approximately 10% at room temperature (300 K) compared to quantum statistics.
Relevance to 6CCVD: Although focused on silicon, the methodology for accurately modeling phonon transport and elastic properties is directly applicable to CVD diamond (C), the material with the highest known thermal conductivity, requiring ultra-high purity materials for experimental validation.
6CCVD Value Proposition: 6CCVD provides the high-purity Single Crystal Diamond (SCD) and Polycrystalline Diamond (PCD) required to experimentally validate and extend these advanced thermal transport models in real-world, high-performance applications.

Technical Specifications

The following table summarizes key numerical results and parameters achieved by the optimized minimal Tersoff potential compared to experimental reference data for diamond silicon.

Parameter	Value (Minimal Tersoff)	Unit	Context / Experimental Reference
Thermal Conductivity ($\kappa$)	~61	W/mK	Predicted value at 700 K. Experimental reference: 51 W/mK.
Thermal Conductivity ($\kappa$)	~143	W/mK	Predicted value at 300 K (using quantum statistics).
Classical Underestimation	~10	%	Amount by which classical statistics underestimates $\kappa$ at 300 K.
Lattice Constant ($a$)	5.434	Å	Calculated value. Matches experimental reference (5.43 Å) closely.
Cohesive Energy ($E_c$)	-4.63	eV/atom	Calculated value. Matches experimental reference (-4.63 eV/atom).
Elastic Constant $C_{11}$	148	GPa	Calculated value. Experimental reference: 167.4 GPa.
Elastic Constant $C_{12}$	65	GPa	Calculated value. Experimental reference: 65.2 GPa.
Elastic Constant $C_{44}$	75	GPa	Calculated value. Experimental reference: 79.6 GPa.
Minimal Potential Parameters	6	Dimensionless	Reduced from 9 (original Tersoff) or 17 (latest variants).
Simulation Temperature Range	300 to 1000	K	Range used for Molecular Dynamics (MD) simulations.

Key Methodologies

The research utilized a combination of quantum mechanics (DFT) and classical simulation techniques (MD, PBTE) optimized by a genetic algorithm (GA) running on GPUs.

Training Data Generation (DFT):
- Tool: Vienna Ab initio Simulation Package (VASP).
- Functional: Revised GGA-PBE (GGA-PBEsol) chosen for accurate lattice constant prediction.
- Data Types: Energy, virial, and force data calculated for many configurations, including triaxial, biaxial, and uniaxial deformations, and various silicon allotropes (simple cubic, BCC, FCC, silicene).
- Force Optimization: Stopping criteria set for forces < 10^-4 eV/Å.
Parameter Optimization (Genetic Algorithm):
- Tool: GPUGA (Graphics Processing Units Genetic Algorithm), an efficient open-source code.
- Objective Function: Fitness function minimized based on a weighted sum of errors for energy, virial, and force data compared to DFT results.
- Parameters: Minimal Tersoff potential optimized using 6 essential fitting parameters ($D_0, a, r_0, \beta, \eta, h$).
Thermal Property Evaluation (MD & PBTE):
- MD Tool: GPUMD (Graphics Processing Units Molecular Dynamics) open-source code.
- MD Method: Homogeneous Nonequilibrium Molecular Dynamics (HNEMD) used for many-body potentials.
- PBTE Method: Peierls-Boltzmann Transport Equation solved iteratively, considering three-phonon and four-phonon scattering, allowing for comparison between classical and quantum statistics.
- Simulation Setup: Simulation cell size of 8000 silicon atoms with periodic boundary conditions.
- Isotope Scattering: Included in simulations to match experimental conditions (92.2% ²⁸Si, 4.7% ²⁹Si, 3.1% ³⁰Si).

6CCVD Solutions & Capabilities

The accurate modeling of thermal transport and elastic properties, as demonstrated in this paper, is foundational for developing next-generation thermal management and high-power electronic devices. 6CCVD specializes in providing the highest quality MPCVD diamond materials necessary to validate and apply these theoretical insights.

Applicable Materials for Experimental Validation

While the paper models diamond silicon, the principles of accurate phonon dispersion are paramount for understanding and optimizing the performance of actual CVD diamond (Carbon), which exhibits the highest thermal conductivity of any known material.

6CCVD Material	Recommended Grade	Relevance to Research
Single Crystal Diamond (SCD)	High Purity Thermal Grade	Ideal for validating thermal transport models. SCD offers the highest intrinsic thermal conductivity (up to 2200 W/mK) and minimal defects, allowing researchers to isolate and study fundamental phonon scattering mechanisms modeled in the paper.
Polycrystalline Diamond (PCD)	Optical/Thermal Grade	Suitable for large-area applications (up to 125mm) where bulk elastic and thermal properties are critical. PCD allows for the study of grain boundary scattering effects, which are analogous to the boundary conditions modeled in MD simulations.
Boron-Doped Diamond (BDD)	Heavy Boron Doped	Relevant for extending the research into electro-thermal coupling. BDD is a conductive semiconductor, allowing for studies of how doping and electronic carriers affect phonon transport and elastic constants.

Customization Potential & Engineering Support

The research highlights the sensitivity of thermal properties to material structure and boundary conditions. 6CCVD offers specialized manufacturing capabilities to meet the precise requirements of advanced thermal physics research:

Custom Dimensions and Thickness: 6CCVD can supply SCD and PCD plates/wafers in custom dimensions, including large-area PCD up to 125mm, and precise thickness control for both SCD and PCD (0.1µm to 500µm). This is crucial for controlling boundary scattering effects in experimental thermal measurements.
Ultra-Low Roughness Polishing: We provide industry-leading polishing services, achieving surface roughness (Ra) < 1nm for SCD and < 5nm for inch-size PCD. Minimizing surface roughness is essential for accurate phonon transport studies, as surface scattering can dominate thermal resistance in thin films.
Custom Metalization: For integrating diamond into thermal or electronic devices, 6CCVD offers in-house metalization capabilities, including Au, Pt, Pd, Ti, W, and Cu layers, enabling direct integration with experimental setups or device prototypes.
Engineering Support: 6CCVD’s in-house PhD team specializes in the growth and characterization of MPCVD diamond. We offer consultation services to assist researchers in selecting the optimal material specifications (purity, orientation, thickness) for similar Phonon Transport and Thermal Management projects, ensuring experimental results align with advanced theoretical models.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Silicon is an important material and many empirical interatomic potentials have been developed for atomistic simulations of it. Among them, the Tersoff potential and its variants are the most popular ones. However, all the existing Tersoff-like potentials fail to reproduce the experimentally measured thermal conductivity of diamond silicon. Here we propose a modified Tersoff potential and develop an efficient open source code called GPUGA (graphics processing units genetic algorithm) based on the genetic algorithm and use it to fit the potential parameters against energy, virial and force data from quantum density functional theory calculations. This potential, which is implemented in the efficient open source GPUMD (graphics processing units molecular dynamics) code, gives significantly improved descriptions of the thermal conductivity and phonon dispersion of diamond silicon as compared to previous Tersoff potentials and at the same time well reproduces the elastic constants. Furthermore, we find that quantum effects on the thermal conductivity of diamond silicon at room temperature are non-negligible but small: using classical statistics underestimates the thermal conductivity by about 10% as compared to using quantum statistics.

Tech Support

Original Source

DOI: https://doi.org/10.1088/1361-648x/ab5c5f